Free Printable Pre-Calculus Units 1-3 Extra Credit

1.

What is the equation of the horizontal asymptote?

a)

y = 0

b)

y = -2

c)

y = 2

d)

There isn't one

2.

What is the equation of the vertical asymptote?

a)

x = 0

b)

x = 4

c)

x = -1, x = 4

d)

x = -1

3.

Find the x-intercept(s), if one exists.

a)

(1, 0)

b)

(-1, 0)

c)

(1, 0), (-1, 0)

d)

(0, 0), (1, 0)

4.

What are the coordinates of the y-intercept, if one exists.

a)

(0, 0)

b)

(0, 1)

c)

(0, -1)

d)

there isn't one

5.

What are the coordinates of the hole, if one exists.

a)

(-1, -2)

b)

(-1, ½)

c)

(-1, -½)

d)

there isn't one

6.

What is the equation of the vertical asymptote?

a)

x = 3

b)

x = -3

c)

x = 0

d)

x = -2

7.

What are the x and y intercepts?

a)

(4, 0) and (0, -4)

b)

(-4, 0) and (0, -4)

c)

(-4, 0) and (0, 4)

d)

(0, 0) and (0, -4)

8.

What is the equation of the graph?

a)

b)

c)

d)

9.

What's the horizontal asymptote of the function?

a)

y = 0

b)

No horizontal asymptote

c)

y = 1

d)

y = 9

10.

What's the vertical asymptote of the function?

a)

x = -9

b)

x = 9

c)

x = 3 , x = -3

d)

x = 3

11.

What are the asymptotes

a)

x=1, x= 2, y =1, y= 2

b)

x= 2, x=-2, y = 1

c)

x=2 y =-1

d)

x=1 y =2, y =-2

12.

a)

{-2, 3, 7}

b)

[-2, 3]

c)

{1, 2, 2, 3, 4}

d)

[1, 4]

13.

a)

{1, 2, 3, 4, 5}

b)

{-1, 1, 2, 3}

c)

{1, 2, 3, 5}

d)

[1, 5]

14.

What are the transformations of this functions compared to the parent function?

a)

Shifted right 5, shifted down 2, and reflected over the x-axis

b)

Reflected over the x-axis, vertical stretch by 2, and shifted right 5

c)

Reflected over the x-axis, vertical stretch by 2, and shifted left 5

d)

Shifted right 5, shifted down 2

15.

Which equation matches the transformation described?

a)

b)

c)

d)

16.

Solve.

a)

no solution

b)

6

c)

3

d)

4

17.

a)

A

b)

B

c)

C

d)

D

18.

Name the parent function.

a)

cube root

b)

quadratic

c)

cubic

d)

square root

e)

linear

19.

Which of the following is the domain shown in the graph?

a)

[4,∞)

b)

[-4,∞)

c)

(4,8)

d)

[-4,8]

20.

Find the domain and range of the function.

a)

Domain: (-∞, ∞)

Range: [-∞, 4]

b)

Domain: [1, ∞)

Range: (-∞, 4]

c)

Domain: [-1. ∞)

Range: [4, ∞)

d)

Domain: [4, ∞)

Range: [-1,∞)

21.

What is the domain of the parabola created by the ball?

a)

Domain : 0 ≤ d ≤ 280

b)

Domain : 0 ≤ h ≤ 150

c)

Domain : 0 ≤ d ≤ 570

d)

Domain : 0 ≤ h ≤ 280

22.

What is the range of the graph?

a)

All real numbers

b)

0 ≤ x ≤ 4

c)

0 ≤ x ≤ 2000

d)

0 ≤ y ≤ 2000

23.

f(x-2)

a)

2x² - 13x + 18

b)

2x² - 5x + 18

c)

2x² - 8x + 3

d)

2x² - 13x + 2

24.

Find f[g(5)]

a)

30

b)

242

c)

92

d)

2

25.

a)

24

b)

96

c)

2

d)

-4

e)

4

26.

Find the inverse of f(x) = -3x²+5

a)

b)

c)

d)

27.

a)

3

b)

1

c)

4

d)

None of the Above

28.

a)

7

b)

6

c)

11

d)

None of the Above

29.

a)

6

b)

8

c)

15

d)

None of the Above

30.

Find the inverse.

a)

A

b)

B

c)

C

d)

D

31.

Find the inverse.

a)

A

b)

B

c)

C

d)

D

32.

If $f\left(x\right)=\frac{1}{x}$ and $g\left(x\right)=3x+2$ find $\left(g\circ f\right)\left(x\right)$

a)

$\frac{1}{3x}+2$

b)

$3x+2$

c)

$\frac{3}{x}+2$

d)

$\frac{1}{3x+2}$

33.

Given f and g in the graph,

what is f(g(2)) ?

a)

3

b)

8

c)

1

d)

4

34.

Given f and g in the graph,
what is $\left(f\circ g\right)\left(-1\right)?$

a)

1

b)

4

c)

-1

d)

6

35.

What is the first step when solving the radical equation $4\sqrt{x-7}+\ 12\ =\ 28$

a)

Divide both sides of the equation by 4

b)

Square both sides of the equation

c)

Subtract 12 from both sides of the equation

d)

Add 7 to both sides of the equation

e)

Check your solution

36.

What are the asymptotes?

a)

x = -3 y = 1

b)

x = 3 y = 1

c)

x = -3 y = -1

d)

x = 3 y = -1

37.

What are the missing values if g(x)=f^-1(x)?

a)

(9,-5)

b)

(-9,-5)

c)

(5,9)

d)

(-9,5)

38.

a)

b)

c)

d)

39.

a)

b)

c)

d)

40.

Was the inverse function found correctly?

a)

no,

b)

yes

41.

Factor

7w³-14w

a)

7w(w²-2)

b)

7w(w²-2w)

c)

7w(w-2)

d)

7w(w+2)

42.

Factor
3a² + 4a + 1

a)

(7a-10)(a-8)

b)

Not factorable

c)

(3a+1)(a+1)

d)

(3a-1)(a-1)

43.

Factor:
4x²-16x-9

a)

(2x-9)(2x+1)

b)

(2x+9)(2x-1)

c)

(4x-1)(x+9)

d)

(x+1)(4x-9)

44.

Solve 6x²-x=2

a)

x= -2/3, 1/2

b)

x= 2/3, -1/2

c)

x= -2/3, -1/2

45.

Solve 3x²-48=0

a)

x= 4, 4

b)

x= -4, -4

c)

x= -4, 4

46.

Solve by factoring: 4x² - 2 = -11x + 1

a)

x = -3/4 and x = -1

b)

x = 4 and x = 3

c)

x = 1/4 and x = -3

d)

x = -1/4 and x = 3

47.

Factor: 3x²- 6x - 24

a)

(3x - 8)(x + 3)

b)

(3x + 4)(x - 6)

c)

3(x - 2)(x + 4)

d)

3(x + 2)(x - 4)

48.

What is the y-intercept of the function?

a)

2

b)

3

c)

1

d)

-2

49.

What is the x-intercept of the exponential function?

a)

(0,1)

b)

(0,0)

c)

There is not one

50.

Given y=4^(x+1)determine the y-intercept

a)

(0,1)

b)

(0,4)

c)

(4,0)

d)

(1,0)

51.

Which equation matches the graph?

a)

y = 2^x+3

b)

y = 2^x + 3

c)

y = 2^x

d)

y = 2^-x

52.

What is the range of y=2^x+1-3?

a)

(-∞,∞)

b)

(-3, ∞)

c)

(-1, ∞)

d)

(-∞, -3)

53.

What is the transformation?

a)

Vertical Translation up 2 and Horizontal translation right 1

b)

Vertical Translation down 2 and Horizontal Translation left 1

c)

Horizontal Translation left 2 and Vertical Translation up 1

d)

Horizontal Translation right 2 and Vertical Translation down 1

54.

What is the range of this function?

a)

(-∞,0)

b)

(0,∞)

c)

(-∞,4)

d)

(4,∞)

55.

State the interval of increasing/decreasing

a)

(∞, -∞)

b)

(-∞,∞)

56.

What transformations have happened to f(x) = 2^x if the new equation is
g(x) = -2^(x+3) -6

a)

It stayed the same

b)

reflects, up 3, left 6

c)

reflects, right 3, down 6

d)

reflects, left 3, down 6

57.

Determine the range for the function
f(x)=3(2)^x-4+5

a)

[5,∞)

b)

(5,∞)

c)

[4,∞)

d)

(4,∞)

58.

Determine the domain for the function
f(x)=3(2)^x-4+5

a)

[5,∞)

b)

(5,∞)

c)

(-∞,∞)

d)

(∞,-∞)

59.

Determine the asymptote for the function
f(x)=3(2)^x-4+5

a)

x=4

b)

y=4

c)

x=5

d)

y=5

60.

Write in exponential form.
log₂32 = 5

a)

2^-5 = 32

b)

2³² = 5

c)

2⁵ = 32

d)

32⁵ = 2

61.

Which equation is depicted by this graph?

a)

y = 3^x+ 2

b)

y = -3^x - 2

c)

y = -3^x+ 2

d)

y = 3^x - 2

62.

Which graph depicts the function y = 3(2)^x+3 - 4

a)

b)

c)

d)

63.

Choose all functions that have a range of $\left(0,\ \infty\right)$

a)

y = 4^x + 2

b)

y = 4^x+2

c)

y = 4^x-2

d)

y = -4^x

e)

y = (1/4)^x

64.

Solve for x.
4^x = ¹/₁₆

a)

2

b)

-2

c)

1/2

d)

4

65.

What is the asymptote?

a)

x=0

b)

y=0

c)

x=1

d)

y=1

66.

Find the intervals of concavity for

f(x) = x² + 2x + 1.

a)

concave up: (-∞,∞)

b)

concave down: (-∞,∞)

c)

concave up: (2, ∞)

concave down: (-∞,2)

d)

concave up: (-∞,2)

concave down: (2, ∞)

67.

Over what intervals is f(x) decreasing?

a)

(-∞, -1) ∪ (1, ∞)

b)

(-∞, -√3) ∪ (0, √3)

c)

(-1, 1)

d)

(-√3, 0) ∪ (√3, ∞)

68.

What is the increasing interval(s) on the function shown?

a)

$\left(-\infty,\ -15\right)\ and\ \left(9,\ -15\right)$

b)

$\left(-2,\ 9\right)\ and\ \left(2,\ \infty\right)$

c)

$\left(-\infty,\ -2\right)\ and\ \left(0,\ 2\right)$

d)

$\left(-2,\ 0\right)\ and\ \left(2,\ \infty\right)$

69.

What are the increasing intervals?

a)

(- ∞, 0) & (2, ∞ )

b)

(-1, 0) & (2,4)

c)

(0,2) & (-3, -7)

d)

(-8, -3) & (-7, 8)

70.

This graph is positive on the intervals...

a)

( -∞, -2 ) U ( 2, ∞ )

b)

( 4, ∞ )

c)

( -2, 2 )

d)

( -∞, 4 )

71.

What is the end behavior of the graphed function as x approaches negative infinity?

a)

y approaches negative infinity

b)

y approaches positive infinity

c)

y approaches 2

d)

y approaches -1

e)

Does Not Exist

72.

Identify the intervals where the graph is negative. Check all that apply.

a)

$\left(-\infty,-1\right)$

b)

$\left(-1,\infty\right)$

c)

$\left(-3,1\right)$

d)

$\left(-\infty,-3\right)$

e)

$\left(1,\ \infty\right)$

73.

Identify the intervals where the graph is positive. Check all that apply.

a)

$\left(-\infty,0\right)$

b)

$\left(0,4\right)$

c)

$\left(4,\infty\right)$

d)

$\left(-\infty,2\right)$

e)

$\left(2,\infty\right)$

74.

Which is the correct notation for the "limit of f(x) as x approaches 3 is 7"?

a)

$\lim_{x\rightarrow7}f\left(x\right)=3$

b)

$\lim_{ }f\left(3\right)=7$

c)

$f\left(3\right)=7$

d)

$\lim_{x\rightarrow3}f\left(x\right)=7$

75.

What is the end behavior on the left side

a)

$\lim_{x\rightarrow\infty}f\left(x\right)=\infty$

b)

$\lim_{x\rightarrow-\infty}f\left(x\right)=-\infty$

c)

$\lim_{x\rightarrow-\infty}f\left(x\right)=\infty$

d)

$\lim_{x\rightarrow\infty}f\left(x\right)=\infty$

76.

$\lim_{x\rightarrow-\infty}f\left(x\right)=$

a)

$-\infty$

b)

$\infty$

c)

$0$

d)

$DNE$

77.

$\lim_{x\rightarrow\infty}f\left(x\right)\ =\ ?$

(a)

78.

What is the Vertical Asymptote?

a)

x=5

b)

x=0

c)

y=0

d)

x=1

79.

What is the equation of the asymptote?

a)

x = -3

b)

x=5

c)

y= -3

d)

y=5

80.

Which equation is the inverse of the equation above?

a)

b)

c)

d)

81.

Logarithms are the inverse of ___________.

a)

Natural Log

b)

Quadratics

c)

Radicals

d)

Exponentials

82.

Find the Inverse of $y\ =\ \log_4\left(x-1\right)$

a)

$y=x$

b)

$y=\log_34^x$

c)

$y=4^x+1$

d)

$y=4^{x+1}$

83.

Find the inverse of $y=\ln\left(x+3\right)$

a)

$y=e^x-3$

b)

$y=e^{x-3}$

c)

$y=e^x+3$

d)

$y=e^{x+3}$

84.

Simplify: $e^{\ln40\ }$

a)

40

b)

-40

c)

e

d)

ln

85.

Simplify the following logarithmic function:
log₂2⁸=

a)

8

b)

2

c)

1

d)

16

86.

List the range for the following.

a)

(-∞,∞)

b)

(-1, ∞)

c)

(5,∞)

d)

(1, ∞)

87.

List the domain for the following.

a)

(-∞,∞)

b)

(-1, ∞)

c)

(5,∞)

d)

(1, ∞)

88.

Find the inverse of: y = 7^x +6

a)

b)

c)

89.

Which has a vertical asymptote?

a)

exponential

b)

logarithm

c)

both

90.

Which has a horizontal asymptote?

a)

exponential

b)

logarithm

c)

both

91.

Over the interval (−1, 2), the graph of the polynomial shown could be described as

a)

decreasing

b)

increasing

c)

positive

d)

negative

92.

You want to make a box to contain dirt and your pet earthworm. Using a 7 in by 10 in rectangle of cardboard, you cut congruent squares from the corners and fold up the sides. Which of the following is the function that will find the maximum volume?

a)

$V=\left(7-2x\right)\left(10-2x\right)$

b)

$V=x\left(7-2x\right)\left(10-2x\right)$

c)

$V=x\left(7-x\right)\left(10-x\right)$

d)

$V=x\left(7+2x\right)\left(10+2x\right)$

93.

A farmer wants to construct a rectangular pigpen using 400 ft of fencing. The pen will be built next to an existing stone wall, so only three sides of fencing need to be constructed to enclose the pen. What dimensions should the farmer use to construct the pen with the largest possible area?

a)

100ft x 200ft

b)

102ft x 196 ft

c)

50 ft x 300 ft

d)

50 ft x 175 ft

94.

We want to construct a box whose base length is 3 times the base width. If the box must have a volume of 50 ft³, determine the dimensions that will minimize the amount of material used.

a)

w=2.027ft, h=4.055ft, l=6.082ft

b)

w=1.488ft, h=3.347ft, l=6.694ft

c)

w=2.231ft, h=3.347ft, l=6.694ft

d)

w=0.485ft, h=2.111ft, l=4.222ft

95.

(3+8i)(-2-i)

a)

2-19i

b)

23-i

c)

34+5i

d)

23-i

96.

Simplify:
(10+ 15i) - (48 - 30i)

a)

58 - 45i

b)

58 - 15i

c)

-38 - 15i

d)

-38 + 45i

97.

\left(x-6\right)\left(x+2\right)\left(x-2\right)<0

Find the solutions of the above inequality.

a)

$\left(-\infty,-1\right)\cup\left(1,5\right)$

b)

$\left(-2,2\right)\cup\left(6,\infty\right)$

c)

$\left(-2,2\right)\cup\left(6,\infty\right)$

d)

$\left(-\infty,-2\right)\cup\left(2,6\right)$

98.

What are the solutions for the polynomial inequality?
$-2x^3+2x^2+4x<0$

a)

$\left(-1,\ 0\right)\cup\left(2,\ \infty\right)$

b)

$\left(-\infty,\ -1\right)\cup\left(0,\ 2\right)$

c)

$\left(2,\ \infty\right)$

d)

$\left(-1,\ 2\right)\cup\left(2,\ \infty\right)$

99.

Solve the rational inequality and state your solution in interval notation.

$\frac{-x}{x-3}\ge0$

a)

$\left(0,\ +\infty\right)$

b)

$\left[0,\ 3\right)$

c)

$\left(-\infty,\ 0\right)\cup\left(3,\ +\infty\right)$

d)

$\left(-\infty,\ 0\right]\cup\left[3,\ +\infty\right)$

100.

Solve the rational inequality and state your solution in interval notation.

$\frac{3x-7}{x+2}>0$

a)

$\left(-2,\ \frac{7}{3}\right)$

b)

$\left(\ \frac{7}{3},\ +\infty\right)$

c)

$\left(-\infty,-2\right)\cup\left(\frac{7}{3},\ +\infty\right)$

d)

$\left(-\infty,-2\right)\cup\left[\frac{7}{3},\ +\infty\right)$

101.

Solve the rational inequality and state your solution in interval notation.

$\frac{x^2+4x-12}{x^2-4x+4}>0$

a)

$\left(-\infty,\ -2\right]\cup\left[6,\ +\infty\right)$

b)

$\left(-\infty,\ -2\right)\cup\left(6,\ +\infty\right)$

c)

$\left(-\infty,\ -6\right]\cup\left[2,\ +\infty\right)$

d)

$\left(-\infty,\ -6\right)\cup\left(2,\ +\infty\right)$

102.

Which statements below describe the domain of the rational function.
$f(x)=\frac{x^3}{x^2-9}$

Check all that apply.

a)

$x\ne3$

b)

$x\ne\pm3$

c)

$\left(-\infty,\ 3\right)\cup\left(3,\ +\infty\right)$

d)

$\left(-\infty,\ -3\right)\cup\left(3,\ +\infty\right)$

e)

$\left(-\infty,\ -3\right)\cup\left(-3,3\right)\cup\left(3,\ +\infty\right)$

103.

What are the x-intercepts for the rational function?
$f\left(x\right)=\frac{x^2-2x-8}{3x-2}$

a)

$\left(\frac{2}{3},\ 0\right)$

b)

$\left(-\frac{2}{3},\ 0\right)$

c)

$\left(-4,\ 0\ \right)\ \left(2,\ 0\right)$

d)

$\left(4,\ 0\ \right)\ \left(-2,\ 0\right)$

104.

The profit from selling local ballet tickets depends on the ticket price. Using past receipts, we find that the profit can be modeled by the function p= -15x² +600x +60 , where x is the price of each ticket. What is the maximum profit you can make from selling tickets?

a)

$6060

b)

$20

c)

$600

d)

$10,250

105.

Check all the intervals where this graph is increasing.

a)

(-∞, -1)

b)

(-1, 0)

c)

(0, 1)

d)

(1, ∞)

106.

What is the Range of the function being graphed?

a)

(-∞, ∞)

b)

(7, ∞)

c)

(-∞, 7)

d)

(-1, 1)

107.

What are the asymptotes?

a)

x=1, x= 2, y =1, y= 2

b)

x= 2, x=-2, y = 1

c)

x=2 y =-1

d)

x=1 y =2, y =-2

108.

What is the relative min?

a)

(0, 36)

b)

(-2.55, -6), (2.55, -6)

c)

(-∞, ∞)

d)

None

109.

What are all the y-intercepts?

a)

(0, -6.25)

b)

(-3,0), (-2,0), (2,0), (3,0)

c)

(0, 36)

d)

(-∞, ∞)

110.

State the domain:

a)

(-oo, oo)

b)

(-oo, -2) U (-2, 2) U (2, oo)

c)

(-2, 2)

d)

(-oo, -2) U (2, oo)

Pre-Calculus Units 1-3 Extra Credit

Total questions: 110

Worksheet time: 9hrs 10mins

Similar Resources on Wayground